ABSTRACT
The design of unreinforced arches and vaults characteristically encompasses form-finding and/or other techniques to ensure a state of pure-compression under load, e.g., self-weight, imposed and wind loads. Several analytical and physical modelling methods are reported in the literature, which are mainly based on equilibrium methods (e.g., graphic statics). In this paper, a unique numerical method for the determination of funicular structural forms is presented in which classical structural analysis techniques guide the approach. Initially, an arbitrary starting shape is discretised into a predefined number of elements, and the base reactions and internal bending forces are determined. Subsequently, the position of each element is adjusted by a vertical geometrical step, which is directly dependent on the bending moment magnitude at the relevant point. The base reactions and internal bending forces are determined for the new shape, and adjusted through several iterations until there is zero bending moment and the desired span-height-ratio is achieved. The method is outlined in this paper, and several examples are considered to highlight its application and convenience. The optimised shapes from two case-studies, namely an arch and dome, are compared with solutions derived using thrust-line analysis. The pure-compression shapes obtained with both methodologies are practically identical.
